Problem: 3 people can paint 7 walls in 34 minutes. How many minutes will it take for 4 people to paint 10 walls? Round to the nearest minute.
Answer: We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 7\text{ walls}\\ p &= 3\text{ people}\\ t &= 34\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{7}{34 \cdot 3} = \dfrac{7}{102}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 10 walls with 4 people. $t = \dfrac{w}{r \cdot p} = \dfrac{10}{\dfrac{7}{102} \cdot 4} = \dfrac{10}{\dfrac{14}{51}} = \dfrac{255}{7}\text{ minutes}$ $= 36 \dfrac{3}{7}\text{ minutes}$ Round to the nearest minute: $t = 36\text{ minutes}$